Optimal. Leaf size=19 \[ \frac{x^n (a+b x)^{-n}}{a n} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0145925, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{x^n (a+b x)^{-n}}{a n} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 + n)*(a + b*x)^(-1 - n),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.68159, size = 12, normalized size = 0.63 \[ \frac{x^{n} \left (a + b x\right )^{- n}}{a n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1+n)*(b*x+a)**(-1-n),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.014268, size = 19, normalized size = 1. \[ \frac{x^n (a+b x)^{-n}}{a n} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 + n)*(a + b*x)^(-1 - n),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 20, normalized size = 1.1 \[{\frac{{x}^{n} \left ( bx+a \right ) ^{-n}}{an}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1+n)*(b*x+a)^(-1-n),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35755, size = 30, normalized size = 1.58 \[ \frac{e^{\left (-n \log \left (b x + a\right ) + n \log \left (x\right )\right )}}{a n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-n - 1)*x^(n - 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.222709, size = 43, normalized size = 2.26 \[ \frac{{\left (b x^{2} + a x\right )}{\left (b x + a\right )}^{-n - 1} x^{n - 1}}{a n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-n - 1)*x^(n - 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(-1+n)*(b*x+a)**(-1-n),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (b x + a\right )}^{-n - 1} x^{n - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(-n - 1)*x^(n - 1),x, algorithm="giac")
[Out]